We are given a chessboard with 100 rows and 100 columns. Two squares of the board are said to be adjacent if they have a common side. Initially all squares are white.a) Is it possible to colour an odd number of squares in such a way that each coloured square has an odd number of adjacent coloured squares?b) Is it possible to colour some squares in such a way that an odd number of them have exactly 4 adjacent coloured squares and all the remaining coloured squares have exactly 2 adjacent coloured squares?c) Is it possible to colour some squares in such a way that an odd number of them have exactly 2 adjacent coloured squares and all the remaining coloured squares have exactly 4 adjacent coloured squares? graph theorycombinatorics proposedcombinatorics